Understanding Ohm's Law and Charge Units in Electrodynamics

In summary, the conversation discusses the relationships between current density, force, and unit charge in the context of electromagnetism. The equations \vec J = \sigma \vec f and \vec J = \sigma(\vec E +\vec v X \vec B) are referenced, with the understanding that \vec f represents force per unit charge and that the unit charge is one coulomb. From this, it is concluded that \vec f=\vec E +\vec v X \vec B and that \vec J = \sigma \vec E = \sigma \vec f. The conversation ends with the speaker expressing their realization and understanding of the concept.
  • #1
yungman
5,708
240
This is referring to Chapter 7.1, page 285 of "Introduction of Electrodynamics" 3rd edition by David Griffiths.

[tex]\vec J = \sigma \vec f \;\; \;\;\;\;\;\;\;( \frac{C}{m^2\cdot sec}) [/tex] (1)

Where [itex]f[/itex] is force per unit charge. Is the unit charge one coulomb?.

Also

[tex] \vec J = \sigma(\vec E +\vec v X \vec B)\;\;\;\;\;\;\;\;\;\;\; (\frac{C}{m^2\cdot sec} )[/tex] (2)



My understanding is force:

[tex]\vec F = q(\vec E +\vec v X \vec B) \;\;\;\;\;\;\;\;\;\; \hbox {( N) }[/tex]

For unit charge of one coulomb,

[tex]\vec f = (\vec E +\vec v X \vec B)[/tex] (3)


How do I go from (2) to (3)

Thanks
 
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  • #2
yup, the unit charge is a coulomb

Equation 1 shows how you get from 2 to 3
 
  • #3
LostConjugate said:
yup, the unit charge is a coulomb

Equation 1 shows how you get from 2 to 3

Thanks for the reply.

So if [itex] \vec f[/itex] is unit force which is the force of a coulomb charge.

[tex] \vec F = Q\vec E = 1\;X \;\vec E = \vec E \hbox { for Q = one coulomb }[/tex]?

Therefore

[tex] \vec J \;=\; \sigma \vec E = \sigma \vec f [/tex]

if the velocity of the unit charge is slow and

[tex] Q (\vec v X \vec B) [/tex] is ignored.

Am I getting this right? Just that simple? What was I thinking!:cry::eek:

Thanks

Alan
 

1. What is Ohm's Law?

Ohm's Law is a fundamental law in physics that describes the relationship between voltage, current, and resistance in an electrical circuit. It states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

2. How do I use Ohm's Law to solve problems?

To use Ohm's Law to solve problems, you will need to know two of the three variables: voltage (V), current (I), and resistance (R). You can then use the formula V=IR to calculate the missing variable.

3. What are the units for voltage, current, and resistance?

Voltage is measured in volts (V), current is measured in amperes (A), and resistance is measured in ohms (Ω).

4. What are some real-world applications of Ohm's Law?

Ohm's Law is used in various applications, including designing and analyzing electrical circuits, calculating power and energy consumption, and determining the appropriate size of electrical components for a given circuit.

5. Can Ohm's Law be applied to all electrical circuits?

Yes, Ohm's Law can be applied to all electrical circuits, as long as the conditions are within the linear range of the materials being used. It may not be accurate for non-linear materials, such as diodes and transistors.

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